KYAMBOGO
UNIVERSITY
SCHOOL OF EDUCATION
DEPARTMENT OF PHYSICS
BACHELOR OF EDUCATION (SCIENCES)
COURSE UNIT:
CLASSICAL MECHANICS AND SPECIAL RELATIVITY
COURSE CODE:
SPB 2102
LECTURER’S NAME:
MZ. TR.KABAGAMBE MUGISA MUSA ATWOOKIE
TASK:
PRACTICAL REPORT
NO.
NAME
REGISTRATION NUMBER
1.
DOBA ALLAN
23/U/BED(SCI)/13624/PD
2.
GENZA CYRUS
23/U/BED(SCI)/13630/PD
3.
KAMOGA WILLIAM
23/U/BED(SCI)/13642/PD
4.
KIZZA GERALD
23/U/BED(SCI)/13654/PD
5.
ABITEKANIZA HASSAN
23/U/BED(SCI)/1567/GV
6.
KYEGOMBE ISAAC
23/U/BED(SCI)/13656/PD
7.
NAMBALE PETER MIKE
22/U/BED(SCI)/2193/PD
SIGNATURE
1
TITLE:
AN EXPERIMENT TO VERIFY THE LAW OF CONSERVATION OF MOMENTUM
AND TO SHOW THE CONSERVATION OF KINETIC ENERGY
OBJECTIVE
1. To verify the law of conservation of momentum
2. To show the conservation of kinetic energy for an elastic collision.
THEORY OF THE EXPRIEMENT:
When a body of known mass is in motion with a known velocity, it possesses a physical property
called momentum which is an attribute of its mass and velocity related with the equation
𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚 = 𝑚𝑎𝑠𝑠 𝑥 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦.
When two bodies called, the bodies move with different velocities after collision and hence their
individual momentums change. However, the total linear momentum remains constant assuming
no dissipative forces act on the system.
The experiment to verify the law of conservation of momentum and energy typically involves an
isolated system where two objects collide, often on a frictionless surface. The goal is to
demonstrate that in an isolated system with no external forces, the total momentum remains
constant and for elastic collision where bodies separate after collision, the kinetic energy remains
constant as well.
Theory of Conservation of Momentum
Whether bodies separate after collision (elastic collision) of stick together and move with a
common velocity after collision (inelastic collision), According to the law of conservation of
2
momentum, the total momentum of an isolated system in a given direction remains constant if no
external forces are acting on it. This can be mathematically expressed as:
𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑡𝑜𝑡𝑎𝑙 𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚
𝑓𝑖𝑛𝑎𝑙 𝑡𝑜𝑡𝑎𝑙 𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚
(
)=(
)
𝑖𝑛 𝑎 𝑔𝑖𝑣𝑒𝑛 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛
𝑖𝑛 𝑡ℎ𝑒 𝑠𝑎𝑚𝑒 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛
If two objects with masses 𝑚1 and 𝑚2 collide with initial velocities 𝑢1 and 𝑢2 , and they acquire
velocities 𝑣1 and 𝑣2 after the collision, then:
𝑚1 𝑢1 + 𝑚2 𝑢2 = 𝑚1 𝑣1 + 𝑚2 𝑣2
Theory of Conservation of Energy
Kinetic energy is only conserved in a perfectly elastic collision as for an inelastic collision, energy
if lost in overcoming friction and other forms of energy like sound and heat.
In an elastic collision, the law of conservation of kinetic energy states that the total kinetic energy
before the collision is equal to the total kinetic energy after the collision. This can be expressed as:
𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝐾𝑖𝑛𝑒𝑡𝑖𝑐 𝐸𝑛𝑒𝑟𝑔𝑦 = 𝐹𝑖𝑛𝑎𝑙 𝐾𝑖𝑛𝑒𝑡𝑖𝑐 𝐸𝑛𝑒𝑟𝑔𝑦
For two objects colliding elastically:
1
1
1
1
𝑚1 𝑢12 + 𝑚2 𝑢22 = 𝑚1 𝑣12 + 𝑚2 𝑣22
2
2
2
2
To verify the law of conservation of momentum and energy in a laboratory, a common approach
is to use a collision experiment. In such an experiment, two objects collide, and we measure their
velocities before and after the collision. The setup and numerical findings can be summarized as
follows:
MATERIALS
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2-3 marbles
A flat table or surface
A ruler or meter stick
A stopwatch (optional)
PROCEDURE:
1. Place two marbles on the table, about 10 cm apart.
2. Measure and record the initial distance between the marbles.
3. Push one marble gently towards the other, making them collide.
4. Measure and record the final distance between the marbles after the collision.
5. Repeat steps 3-4 several times, varying the initial velocity of the pushed marble.
6. If possible, use a stopwatch to measure the time it takes for the marbles to collide and separate.
DATA ANALYSIS:
Let;
d1
:
distance of separation of the marbles
before collision.
d2
:
distance moved by the first marble after
collision.
d3
:
distance the second marble moves after
collision.
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t1
:
time the first marble takes to hit the second
marble.
t2
:
time the first marble takes to stop moving
after collision.
t3
:
time the second marble takes to stop
moving after collision.
Table 1: Showing distances travelled and respective time taken.
Trial
d1(m)
d2(m)
d3(m)
t1(s)
t2(s)
t3(s)
1
0.100
0.020
0.160
0.82
1.81
2.37
2
0.200
0.150
0.390
0.41
2.06
4.61
3
0.300
0.350
0.510
0.51
3.50
3.61
4
0.400
0.425
0.705
0.83
4.40
5.50
5
0.500
0.155
0.408
1.20
2.68
4.40
6
0.600
0.130
0.497
1.30
2.72
4.19
Finding the initial and final velocities of the marbles before and after collision using the formula;
𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 =
𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡
𝑡𝑖𝑚𝑒
And we consider the average velocity.
Finding the initial and final momentum using the formular;
𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚 (𝑃) = 𝑚𝑎𝑠𝑠 𝑥 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦
5
𝑢1
:
initial velocity of the first marble before
collision.
𝑣1
:
final velocity of the first marble after
collision.
𝑣2
:
final velocity of the second marble after
collision.
m
=
mass of each marble.
𝑃1
=
initial momentum.
𝑃2
=
final momentum.
Table 2: Showing initial and final velocities. Initial and final momentum
Trial 𝑢1 (𝑚𝑠 −1 ) 𝑣1 (𝑚𝑠 −1 ) 𝑣2 (𝑚𝑠 −1 ) 𝑃1 (𝑘𝑔𝑚𝑠 −1 ) 𝑃2 (𝑘𝑔𝑚𝑠 −1 )
1
0.12
0.02
0.13
0.12m
0.15m
2
0.49
0.15
0.17
0.49m
0.32m
3
0.59
0.20
0.28
0.59m
0.48m
4
0.48
0.19
0.26
0.48m
0.45m
5
0.42
0.12
0.19
0.42m
0.31m
6
0.46
0.10
0.24
0.46m
0.34m
The results indicate that momentum was conserved since the initial momentum in each trial is
approximately equal to the final momentum.
Finding initial and final kinetic energies using the formular;
6
1
𝑘𝑖𝑛𝑒𝑡𝑖𝑐 𝑒𝑛𝑒𝑟𝑔𝑦 = 2 (𝑚𝑎𝑠𝑠)𝑥(𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦)2
Table 3: Showing the initial and final kinetic energy.
k1
=
total kinetic energy before collision
k2
=
total kinetic energy after collision.
Trial
k1(J)
k2(J)
1
0.0144
0.0173
2
0.2401
0.0514
3
0.3481
0.1184
4
0.2304
0.1037
5
0.1764
0.0505
6
0.2116
0.0676
The results indicate that kinetic is conserved since the initial total kinetic energy in each trial is
approximately equal to the final total kinetic energy.
GENERAL DISCUSSION OF RESULTS:
The results indicate that momentum was conserved. Although in most trials, the results were not
correlating, this is because of the following;
•
Friction force between the marbles and the surface of the table leads to lose of some kinetic
energy since the surface that we used was not all that smooth as for the case .
•
Air resistance.
•
There was also inaccurate measurement of time and distances at which the marbles collided
and came to rest.
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Conclusion:
This practical investigation successfully verified the laws of conservation of momentum and
energy through simple experiments with two marbles, aligning with theoretical expectations
outlined in physics principles despite limitations in equipment availability in a poorly stocked lab
setting.
Future experiments could explore additional factors affecting these laws, such as varying masses
or angles of collisions, to further enrich understanding of these fundamental concepts in physics
while considering improvements in measurement techniques for more accurate results.
REFERENCES:
1. Halliday, D., Resnick, R., & Walker, J. (2018). Fundamentals of Physics (11th ed.). Wiley.
2. Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers (10th ed.). Cengage
Learning.
3. Young, H. D., & Freedman, R. A. (2020). University Physics with Modern Physics (15th ed.).
Pearson.
4. Giancoli, D. C. (2014). Physics: Principles with Applications (7th ed.). Pearson.
5. Taylor, J. R. (1997). An Introduction to Error Analysis: The Study of Uncertainties in Physical
Measurements (2nd ed.).
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